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Section #:
Math 165: Final Exam — Part 1
Fall 2014
This part of the exam has 8 problems for a total of 40 possible points. Each problem is
worth 5 points.
You may NOT use a calculator on this section. You must show all work, but you need not
simplify your answers unless instructed to do so. This part of the exam will be collected
after 50 minutes.
Question 1:
Question 2:
Question 3:
Question 4:
Question 5:
Question 6:
Question 7:
Question 8:
40 Total Points:
Z Question 1. Evaluate
Z
Question 2. Evaluate
1
4
1√
π
4x − 3x − 3 x + 2x−1 − 7/2 + 165
3
x
7
3
√
(2 x − 3)3
√
dx.
3 x
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dx.
Question 3. A function F (x) has derivative F 0 (x) = x − 6e2x + 1 and it is known that
F (0) = 0. Find the value of F (2).
Question 4. Find
dy
if y = (x2 +1) tan−1 (x2 +1). There is no need to simplify your answer.
dx
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Question 5. Let
√
f (x) = x ln x
and
x
g(x) = e 10 .
As x → ∞, does f (x) grow faster than g(x), does g(x) grow faster than f (x), or do the two
functions grow at the same rate? Be sure to justify your answer.
Question 6.
Z
a. Let G(z) =
z
2
e−t dt. Find the value of G0 (1). (2 points.)
1
Z
b. The function H is defined by H(z) = ln 3z +
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−t2
e
1
(3 points.)
z
dt . Find the value of H 0 (1).
Question 7. A function g is defined by
(
g(t) =
Z
4t − 3
− cos(πt)
2
g(t) dt.
Calculate the value of
−2
Z
Question 8. Evaluate
4e3x
dx.
e6x + 1
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t<1
t ≥ 1.